High Temperature Superconductors and Energy from Fusion

Alfred Cheung
March 21, 2019

Submitted as coursework for PH241, Stanford University, Winter 2019


Fig. 1: A slab of yttrium barium copper oxide, the high temperature superconductor to be used in the proposal by Coomonwealth Fusion systems in generating the magnetic fields for fusion reactors. (Source: Wikimedia Commons)

One of the biggest challenges in making energy production by nuclear fusion a reality is in generating a strong enough magnetic field to contain the hot plasma. The plasma must be kept at very high temperatures, on the order of hundreds of millions of degrees, to undergo fusion. Therefore, the required magnetic field strengths, and the magnets required to produce them, are very large. Researchers at MIT, in collaboration with a company called Commonwealth Fusion Systems, have proposed a way to overcome this challenge by using yttrium barium copper oxide (YBCO), a high temperature superconductor, to generate the magnetic fields. [1] It represents an interesting (and potentially world-changing) application of research in condensed matter physics to fusion science. In this paper, we will give a non-technical overview of superconductivity and this proposed application.

Superconductors, Magnetic Fields, and Critical Currents

From freshman level physics, a current carrying wire generates a magnetic field. The strength of the generated field is proportional to the magnitude of the current. Thus, the stronger the current, the larger the magnetic field. For confinement of plasma at temperatures high enough for fusion to occur, the field must be of the order of 10 T in strength (for comparison, a refrigerator magnet is of the order 10-2 T). One way to achieve a large current is to use superconductors. A superconductor is a material whose electrical resistance drops to zero below a certain critical temperature. Because of the zero resistance, large, stable currents - and hence large, stable magnetic fields - can be achieved. The critical temperature depends on the specific material. Indeed, traditionally one of the most important technological applications of superconductivity is in generating the magnetic fields used in magnetic resonance imaging. However, it turns out that a superconductor can only remain superconducting up to a certain current strength called the critical current. The critical current is generally higher for superconductors with higher critical temperature. [2]

High Temperature Superconductors

Superconductivity was first discovered in mercury cooled to around 4°K by Kamerlingh Onnes in 1911. [2] In the 70 years after that discovery, many more superconductors were discovered with low critical temperatures typically less than 30°K. In that same period, a very successful theory for understanding these low temperature superconductors was developed. [2] Superconductivity (at least the low temperature "conventional kind") was thought to be understood until 1986 when Bednorz and Muller discovered superconductivity in lanthanum barium copper oxide with a critical temperature of 35°K. [3] Since then, more copper based superconductors were discovered such as YBCO with a critical temperature of 90°K. These "high temperature" superconductors were unique from their conventional counterparts not just in their generally substantially higher transition temperatures, but also their material characteristics (they tend to be brittle ceramics as opposed to metals). Based on the conventional theory, these materials are not expected to be superconducting! To this day, there is still no complete theory for high temperature superconductors.

High Temperature Superconductors and Fusion Reactors

While these is still much ongoing research into how superconductivity is achieved in these materials, the key practical aspect is that they have high critical temperatures, and therefore generally high critical currents. Thus, they can allow for achieving larger magnetic fields (at higher temperatures as compared to low temperature superconductors) needed for containing plasma in fusion reactors. That is the proposal of Commonwealth Fusion Systems. This is in contrast to the ITER project also aimed at realizing a large-scale tokamak fusion reactor. [4] In ITER, the magnetic fields are achieved by using conventional low temperature superconductors, a technology that has been well developed. It remains to be seen which approach (or neither) will be successful in the end.

A general challenge in using high temperature superconductors in practical applications relates to their brittle nature - it is hard to form rigid wires with them. The reactors proposed by Commonwealth will use superconducting "tapes" made from YBCO. [1] The tapes are essentially wires of YBCO which are made possible by encasing the superconducting material as a powder inside a metal tube. These tapes can then be wound into toroidal solenoids to generate large magnetic fields up to around 9.2 T. [1] A slab of YBCO is shown in Fig. 1.


The stated goal of Commonwealth is to build a cheaper and relatively compact tokamak-based fusion generator within 20 years. This is of course exciting from a energy point of view. For researchers in the condensed matter physics community (in which the author is part of), the Commonwealth endeavor also has an extra merit in that, if successful, it would represent a major application of high temperature superconductors, which unfortunately have been quite limited in scope even after 30 years of their discovery.

© Alfred Cheung. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] B. N. Sorbom et al., "ARC: A Compact, High-Field, Fusion Nuclear Science Facility and Demonstration Power Plant with Demountable Magnets," Fusion Eng. Des. 100, 378 (2015).

[2] M. Tinkham, Introduction to Superconductivity (Dover 1996).

[3] J. G. Bednorz and K. A. Müller, "Possible High Tc Superconductivity in the Ba-La-Cu-O System," Z. Phys. B 64, 189 (1986).

[4] J. Chabolla, "International Thermonuclear Experimental Reactor (ITER)," Physics 241, Stanford University, Winter 2017.